Measuring triangle



C HOHMANN MEASURING AtFRIANGLE -Filed Dec. 8, 1921 k.en

Patented ct. 9, 1923.

PATENT orifice.

CHARLES HORMANN, or JERSEY Grrr, NEW JERSEY.

MEASURING TRIANGLE. l

Application filed December 8, 1921. Serial 110.521,02?.l n

T0 all 'whom t may concern: f

Be it known that I, CHARLES HORMANN, a citizen of the United States, and a resident of Jersey City, in the county of Hudson and State of New Jersey, have invented a new and Improved Measuring Triangle, of which the following is a full, clear, and exact description.

This invention relates to a triangle, and has for an object the provision of a triangle so constructed as to the arrangement of its angles and the scales used on it that various information concerning the drawing and plotting of circles can be very simply and readily obtained.

Another object resides 'in the provision of meanswhereby merely laying they triangle in a particular manner on any circle drawn, the circumference of that circle can be obtained by reading a particular scale of the triangle.

A further object resides in the provision of' means whereby the radius of a` circle of any given circumference can be very readily ascertained by meansof marks on the triangle. v y

A stillv further object resides in the particular construction and arrangement of parts `which are hereinafter described and claimed and shown `in the `accompanying drawings.

The invention yisillustrated in the figure,

`which shows the triangle with the scales thereon and three different `sizes of ycircles concerning which the manipulation and observation of the triangle can result in definite information.

The form of the invention shown drawing is a preferred form, although it is understood that modifications inthe construction and arrangement of the parts and in the character of the materials used ma)r be adopted without departing from the` spirit of the invention.

A triangle 1 is formed of any suitable material, preferably a transparent material such as celluloid. The corners 2 and 3 of the triangle are forme-d by equal angles,

namely, 39o each. Consequently the angle in the corner 4t is 1020.

While I have stated that the angle desigf nated by the numeral 2 issubstantially 390, by a more careful calculation this angle is approximately 38 83 3". This was found in the following manner:

The length of the radius between the in the.

numerals 8 and 5 is designatedas unity.

The length of the lines between the numerals 7 and 8 is designated as and when reduced is equa-l to ysaid line (line 5) and by the line between the numerals 7 and 8.

Find the sine of the angledesignated by the numeral 2.

The line between the numeral 7 and l designate by X and the portion of line 6 between 8 and 7 as Y z 1.5708. Theporl tion `of line 5 between 8 at the circurnference A, I designate as M.

Since the sine ofangle 2 is .62321, the angle z 380 33 3- which warrants ap# plicant in stating 'that the equal angles are substantially 39 for practical purposes.

I have shown the circles A, B andC laid out with respect to this triangle, and it is found, for instance, that if the tip of the triangle adjacent the angle 2 be placedi on the circle A at the end of any diameter, and if the edge 5 bel disposed to lie along the diameter of the circle A, then the edge 6, which in this case would be the hypotenuse cf the triangle, would intersect the circumference of the circle at a point 7. rlfhe distance of the point 7 from the point 8, they tip of the triangle, would be equal to thek sidey of a square the perimeter 'ofwhich would be equal to the circumference of this circle A. Therefore, if we multiply this distance in any given unit, such as inches, y,

. edge 10.

sides of the square, the value obtained iii the units, such as inches, will represent the circumference of a circle. Since the distance from 8 to is four inches, the triangle is marked adjacent this point with the numeral 16. This numeral 16 is only one marking or graduation disposed adjacent the edge 6 of the triangle, and these various values, which are shown running from l to 36, represent the circumferences of circles in inches. this edge 6 at the triangle and relates to the length of the sides of equal squares in inches. This second set of markings or graduations is disposed on lines such as 9 which are drawn from the marks of circumference in a direction parallel to the The points Where each of the lines 9 intersects the edge 5 of the triangle are marked withv numbers similar to the numbers at the other end of the line, namely, from l to 36. y The edge 10 is laid out ina scaleI of inches for any convenient use. It is also to be noted that `the length of the line 9 drawn from the numeral lllfon the circumference scale to the saine number'on the edge 5 is tvvo and one-quarter inches. This represents the radius of a circle the circumference of which is fourteen inches. Calculation will prove this to be substantially correct. Therefore, if the tip 8 is laid on the pole of the diameter of any given circle, the circumference can be read by noting the value of the graduation at the point Where the edge 6 intercepts the circumference of the circle, and the radius of the circle can be instantly" located -by following down the line 9 from its graduation to the edge 5. The value of the radius can be ascertained from the scale called Inches of radius disposed near the edge 5 and which represents the respective lengths of the various lines 9 which are equal to the length of the radius of the circle in question.

As a further example of the use of this scale, consider circle B, and assuming that the tip 8 of the triangleis laid at oneend of a diameter of the circle B, the edge 6 intercepts the circumference of the circle B at a point marked on the scale of circumference. This means that the circle B isV twenty-five inches in circumference.

. Reading the scale called Inches of the side of square, We note by following down the line 9 connected to the graduation 25 a little way, that the side of the square corresponding to this` circle is six and onequarter inches. To find the area of the square equal to the area of theV circle, it is merely necessary to square six and onequarter. Following. this line 9 further down, the point Q5 is located. on the ,scale adja cent the; edge 5, Which immediately gives` Another scale is disposed along referred to in the specification and claims is tok be construed as a plate of materialin the shape ofv a triangle.

"What I claim is:

l. A measuring device ivh'icli comprises an isosceles triangle for use inplotting.

circles, the equal angles of the triangle being substantially 390, said triangle being pro vided Avvitli spaced linesparallelv to a side opposite one of the equal angles and cutting the other tivo sides to forml graduations along the longer side and numbered to designate the lengths ofthe circumference of various circles to which' the device may bc4 applied, said parallel lines being numbered. progressively to designate the length of the radii of circles, said parallel linesv being alsok numerically designated to represent the length of a side of a square theI area of which is equal to the areaofa circle defined by the graduations on. the triangle and to l which the device has been applied.

2. A measuring device comprising an isosceles triangle forv use in plottingcircles,

the equal angles of which havey a value of .substantially 39", said triangleV having a scale of graduations along the edgeof its longer side to represent they lengths of the circumference of circles, said triangle being provided with'V a plurality of lines drawn from each graduationI to the opposite side and intercepting said side, the length of each of said sides being equal to the radius of a circle, the circumference of` Which is represented by the first mentioned graduations,

3. A measuring device which comprises an isosceles triangle for use in plotting circles, the equal angles of the triangle being substantially 39o, said triangle being provided with a scale of graduations along one side of the triangle, said scale of graduations representing the circumferences of circles, the. circumference of Which intercepts the side provided with the graduations when the vertex of either of the equal angles is placed at one end of the diameter, With thel adjacent side extending along` the diameter of'said circle..

CHARLES HOHMANN'. 

